539 citations · 6.8k across the 160 of their papers we have counts for
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Periodic minimizers in 1D local mean field theory
Alessandro Giuliani, Joel L. Lebowitz, Elliott H. Lieb
Using reflection positivity techniques we prove the existence of minimizers for a class of mesoscopic free-energies representing 1D systems with competing interactions. All minimiz…
A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy II: Convexity and Concavity
Eric A. Carlen, Elliott H. Lieb
We revisit and prove some convexity inequalities for trace functions conjectured in the earlier part I. The main functional considered is Φ_{p,q}(A_1,A_2,...,A_m) = (trace((\sum_{j…
Symmetry breaking in Laughlin's state on a cylinder
Sabine Jansen, Elliott H. Lieb, Ruedi Seiler
We investigate Laughlin's fractional quantum Hall effect wave function on a cylinder. We show that it displays translational symmetry breaking in the axial direction for sufficient…
Probabilistic coherence and proper scoring rules
Joel Predd, Robert Seiringer, Elliott H. Lieb +3
We provide self-contained proof of a theorem relating probabilistic coherence of forecasts to their non-domination by rival forecasts with respect to any proper scoring rule. The t…
Number of Bound States of Schroedinger Operators with Matrix-Valued Potentials
Rupert L. Frank, Elliott H. Lieb, Robert Seiringer
We give a CLR type bound on the number of bound states of Schroedinger operators with matrix-valued potentials using the functional integral method of Lieb. This significantly impr…
Striped phases in two dimensional dipole systems
Alessandro Giuliani, Joel L. Lebowitz, Elliott H. Lieb
We prove that a system of discrete 2D in-plane dipoles with four possible orientations, interacting via a 3D dipole-dipole interaction plus a nearest neighbor ferromagnetic term, h…
Mueller's Exchange-Correlation Energy in Density-Matrix-Functional Theory
Rupert L. Frank, Elliott H. Lieb, Robert Seiringer +1
The increasing interest in the Mueller density-matrix-functional theory has led us to a systematic mathematical investigation of its properties. This functional is similar to the H…
A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy
Eric A. Carlen, Elliott H. Lieb
We consider the following trace function on n-tuples of positive operators: Φ_p(A_1,A_2,...,A_n) = Trace (\sum_{j=1}^n A_j^p)^{1/p} and prove that it is jointly concave for 0<p\le…